How to copy object(s) to another layer
To copy an object you have to be in Object mode, right click on the object that you want to copy and the press Shift + D to duplicate it first. 

The duplicate will be in grab mode so right click to get out of grab mode without changing its location. 

The object will still be selected but if it isn't, you can look in the Outliner for it. It will have the original object name followed by a number indicating that is a duplicate such as Object.001.

You then press M to bring up the layer move popup menu and click the button for the layer that you want to move it to or alternatively type the number corresponding to the layer.